Problem: Solve for $x$ and $y$ using elimination. ${-2x+5y = 36}$ ${5x-4y = -5}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $2$ ${-10x+25y = 180}$ $10x-8y = -10$ Add the top and bottom equations together. $17y = 170$ $\dfrac{17y}{{17}} = \dfrac{170}{{17}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x+5y = 36}\thinspace$ to find $x$ ${-2x + 5}{(10)}{= 36}$ $-2x+50 = 36$ $-2x+50{-50} = 36{-50}$ $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {5x-4y = -5}\thinspace$ and get the same answer for $x$ : ${5x - 4}{(10)}{= -5}$ ${x = 7}$